In the latest episode of WandaVision, we learned that Vision truly is worthy of Thor's Hammer. Paul Bettany, one of the core members of the MCU, literally from his inception, was having a tough run in his acting career when director Joss Whedon told him that he wanted him to play Vision in Avengers: Age of Ultron. And when he did get an upgrade from an all-sensing AI in service of Tony Stark/Ironman to a wholly self-sustaining android, he got a terrific introduction as a super-powerful sentient being, who could do the impossible. By impossible we mean, lifting Thor's hammer the Mjölnir. Interestingly, the beginning of Age of Ultron had a sequence where Avengers jokingly try to deduce what makes Thor's hammer "exclusive to him" as they all fail to lift it (except Captain America, and you know why).
But, in the mid-sequence, Vision lifts that hammer like nothing, proving his worthiness to rule Asgard and possess the power of Thor. Just like the Avengers, even the fans were made believe that his ability to lift the hammer comes from the power of Mind Stone, which Vision technically embodies and can't survive without (you know that too). It's no blunder that we believed this explanation and called it a satisfactory justification because we never got to explore Vision at a personal level amidst the ever-growing team of superheroes within the Marvel Cinematic Universe. Plus, Mjölnir itself has a mysterious history within the MCU and we certainly can't know how someone's determined to be worthy to wield it.
Moreover, Vision is a human-like synthezoid based on an amalgamation of intellectual and psychological elements drawn from Stark, Banner, Jarvis, and Ultron, while Mind Stone being the source of his knowledge and understanding of his existence. Since his birth itself is a confusing anomaly, his characterization in the MCU has also been somewhat confusing and incomplete. But the sixth episode of MCU Phase 4 Disney+ series WandaVision has answered why Vision is truly worthy of Mjölnir.
WandaVision Proves Vision is Worthy
In WandaVision's latest episode, Vision finds the barrier through the Westview anomaly and deliberately forces himself out of it. Outside Westview, he begins to disintegrate. Darcy Lewis shouts out that "he needs help"; however, even in his dying moments, his last words are, "please, people need help". Though he's later saved by Wanda, it was a selfless act to urge for help, not for himself but people of Westview. It's this deed of self-sacrifice (which is Vision's second) and his immense contemplation towards other people is that makes him worthy enough to wield the power of the hammer.
Even when he first witnesses Norm [Abhilash Tandon] in pain and agony due to Wanda's mind-control, Vision's first statement to Wanda when he confronts her is concerning the state of Norm and other Westview residents. Even then, despite all his love for Wanda, he urges her to right the wrong; however, their conversation is abruptly interrupted by a "mysterious guest".
And that's not the first time he has proven himself "worthy".
How Vision is Worthy for Mjölnir
The only other person to wield Mjölnir after Odin and Thor are Steve Rogers/Captain America. Now, when Rogers was an obvious choice for Mjölnir as he has given more than just his life towards what's ethically and morally correct. He never hesitated from giving his life and going against the barriers of administration and political agendas to do what he thought was good.
But, Rogers has emotions, feelings, and empathy. But Vision seems more inclined towards calculative decision-making. However, while his intellectual abilities help him make better decisions, they also allow him to focus his thoughts on the consequences of those decisions. Since humans are primitive to something so powerful such as the Mind Stone, Vision intends to divert the use of that power towards the better future of humanity. It's also the combined personalities of Stark, Banner, and Jarvis (all of whom fights for good), that he's able to think for the people rather than giving much thought to agendas and acts such as the Accords.
Moreover, Vision does have feelings. The Mind Stone earlier allowed him to understand emotions and then as his other traits and attributes, he got from his human configurators helped him control those emotions. Just because his thoughts are unbiased, doesn't mean he is emotionless. He just has an upper hand over them and he does not easily let these feelings affect his choices (except when he mistakenly shot Rhodey, given his sorrow over Wanda's arrest in Civil War). Regardless, Vision is the epitome of nobility and selflessness.
Vision's Worthiness to Wield Mjölnir In Retrospect
Throughout the MCU, every decision Vision has made is somehow connected to an optimistic approach. Vision can't delve into the future, but his higher intellect allows him to address a situation from all perspectives. He even analyzes how the involvement of others around him impacts the overall issue.
If you remember when Vision introduces himself and explains his existence and purpose to the Avengers, he shows no hatred towards Ultron, but calmly addresses the root of the problem and decides why it's important for Ultron to die for the greater good. As Sokovia collapses, he saves Wanda from amidst the plummeting debris. Even during Ultron's final moments, he tries to reason with him over mankind's potential to do good; however, he has to ultimately destroy him when he doesn't understand. It shows how Vision sees some redeemable quality in even the purest form of evil, thus signifying that he has a greater sense of good (though he doesn't really have a real heart).
Even in Captain America: Civil War, Vision is the only one who's able to thoughtfully process the consequences and advantages of Sokovia Accords, while others got divided among each other due to their heightened emotions in this regard. Though his explanation of Accords cited the direct proportionality between superheroes' actions and consequent wars and catastrophe, he somehow was also concerned that going against the government at that moment would cause the team too much trouble. His care for Wanda and his growing affection towards her also showed that he was worried that Wanda would be an outcast given that she decides to go against the Accords. Though he was unsuccessful in keeping the team intact, he knew what was the right thing to do, even keeping Wanda away from himself when it came to it.
And then of course he gave his life, though in vain, to stop Thanos from getting all six infinity stones by destroying himself. Though we see him begging Wanda to end his life moments before Thanos reaches him and Wanda after he beats others in combat. However, even at the beginning of the threat, Vision promptly comes with the idea of disintegrating himself in order for the Avengers to ensure a win against the Mad Titan.
It's still a mystery how Mjölnir decides whether the person trying to wield it is worthy or not. In comics, the hammer itself has a cosmic, unexplainable history as well. The inscription on the hammer says, "Whosoever holds this hammer, be he worthy, shall possess the power of Thor". However, per MCU canon, it can be deduced that it's the wielder and his acts that make him worthy of wielding the power of Mjölnir. And the way Vision tore through the barrier in WandaVision to get to the bottom of the truth and arrange for help for the rest of the residents is finally an epiphany for viewers as to why Vision deserves to have those powers.